Problem: Simplify the following expression: $\dfrac{96y}{132y^4}$ You can assume $y \neq 0$.
Solution: $ \dfrac{96y}{132y^4} = \dfrac{96}{132} \cdot \dfrac{y}{y^4} $ To simplify $\frac{96}{132}$ , find the greatest common factor (GCD) of $96$ and $132$ $96 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 3$ $132 = 2 \cdot 2 \cdot 3 \cdot 11$ $ \mbox{GCD}(96, 132) = 2 \cdot 2 \cdot 3 = 12 $ $ \dfrac{96}{132} \cdot \dfrac{y}{y^4} = \dfrac{12 \cdot 8}{12 \cdot 11} \cdot \dfrac{y}{y^4} $ $\phantom{ \dfrac{96}{132} \cdot \dfrac{1}{4}} = \dfrac{8}{11} \cdot \dfrac{y}{y^4} $ $ \dfrac{y}{y^4} = \dfrac{y}{y \cdot y \cdot y \cdot y} = \dfrac{1}{y^3} $ $ \dfrac{8}{11} \cdot \dfrac{1}{y^3} = \dfrac{8}{11y^3} $